Haar and Kolmogorov found the necessary and sufficient conditions under which finite-dimensional subspaces in the space of continuous functions on an arbitrary compact set are Chebyshev. In this paper, it is proved that subspaces of Dirichlet series form Chebyshev subspaces in the space of (mathbf{C}(0,infty]) of continuous and bounded functions in the interval ((0,infty)) that have a limit at infinity.
A basic justification model is sharp when the evidence term constructors (cdot,+,!) in it mean exactly the application of modus ponens rule, the union and the verification of evidences. We construct an example of a sharp model for the logic of proofs LP and establish that in any sharp model of LP every proof term is equivalent to some proof polynomial.
Examples of two linear homogeneous differential equations of the third order are constructed, the spectra of the upper strong exponents of oscillation of signs, zeros, and roots of one of which coincide with the set of rational numbers of the segment ([0,1]) and those of the other equation coincide with the set of irrational numbers of the segment ([0,1]) augmented with the number zero.
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：